For the half-filled HH model, when the Coulomb repulsion \(U\)  is much larger than the electron–phonon coupling \(g\) , two electrons with opposite spin directions cannot occupy the same site, and electrons with up spin and those with down spin are aligned in an alternating sequence in the Mott AF phase, whereas when \(g\)  is much larger than \(U\) , two electrons with opposite spin directions occupy the same site with the aid of an LO phonon, and bipolarons are formed in the Peierls CDW phase. Then, between the AF and CDW phases, the existence of a SC state is predicted, which is responsible for the high-temperature SC state of alkali fullerides.[1]}, [2]}, [3]} The role of phonons in the SC state of cuprates has also been investigated along the same lines,[4]}, [5]}, [6]}, [7]}, [8]}, [9]} and the HH model, despite its simplicity, does seem to represent a versatile approach for the investigation of these materials.
